标题： 仙人掌花空间和Bethe向量的单值性 显示英文标题

标题： Cactus flower spaces and monodromy of Bethe vectors

摘要： 我们继续研究在arXiv:2308.06880, arXiv:2407.06424中开始的cactus flower模空间$\overline{F}_n$和Gaudin模型。我们证明实形式$\overline{F}_n(\mathbb{R})$的操持覆盖的同构类与具有某些半单性和有限性条件的具体coboundary张量范畴（即承认到集合上的忠实张量函子的coboundary张量范畴）的等价类自然一一对应。按照arXiv:1708.05105的策略，对于任何复半单李代数$\mathfrak{g}$，我们从非均匀Gaudin模型的Bethe本征线覆盖中恢复Kashiwara$\mathfrak{g}$-晶体，作为一个具体的coboundary范畴。利用这一点，我们计算了三角函数Gaudin模型在两个不同实点上的Bethe本征线的单值群。在最小最高权的特殊情况下，这可以被视为Bezrukavnikov和Okounkov关于仿射Grassmannian切片的极小分解的辛解析量子上同调的墙穿猜想的组合版本。 显示英文摘要

摘要： We continue the study of cactus flower moduli spaces $\overline{F}_n$ and Gaudin models started in arXiv:2308.06880, arXiv:2407.06424. We show that isomorphism classes of operadic coverings of the real form $\overline{F}_n(\mathbb{R})$ are naturally one-to-one with equivalence classes of concrete coboundary monoidal categories (i.e. coboundary monoidal categories that admit a faithful monoidal functor to sets) with certain semisimplicity and finiteness conditions. Following the strategy of arXiv:1708.05105, for any complex semisimple Lie algebra $\mathfrak{g}$, we recover Kashiwara $\mathfrak{g}$-crystals, as a concrete coboundary category, from the coverings given by Bethe eigenlines for inhomogeneous Gaudin models. Using this, we compute the monodromy of Bethe eigenlines for trigonometric Gaudin models over two different real loci. In the particular case of minuscule highest weights, this can be regarded as combinatorial version of the wall-crossing conjecture of Bezrukavnikov and Okounkov for quantum cohomology of symplectic resolutions in the case of minuscule resolutions of slices in the affine Grassmannian.